General Access Structures Research Articles

Secret Sharing Schemes With General Access Structure Based On MSPs

In this paper we introduce two operations of access structure to build large monotone span programsMSPs from small MSPs. Furthermore, we point out a new method of constructing secret sharing schemes realizing any access structure, using MSPs.

An efficient and secure multi-secret sharing scheme with general access structures

A multiple secret sharing scheme can share a group of secrets in each sharing session, which is very useful especially in sharing large secrets. However, most of the existing multiple secret sharing schemes are (t, n) threshold schemes, so they are fit for only threshold applications and unfit for the applications of general access structures. Due to the fact that a (t, n) threshold scheme could only handle a small fraction of the secret sharing idea, a novel multi-secret sharing scheme is proposed, which is designed based on general access structures. The security of this scheme is the same as that of Shamir's threshold secret sharing scheme. Compared with the existing multiple secret sharing schemes, the proposed scheme can provide greater capabilities for many applications because it is able to deal with applications of general access structures.

Secret sharing schemes with partial broadcast channels

In a conventional secret sharing scheme a dealer uses secure point-to-point channels to distribute the shares of a secret to a number of participants. At a later stage an authorised group of participants send their shares through secure point-to-point channels to a combiner who will reconstruct the secret. In this paper, we assume no point-to-point channel exists and communication is only through partial broadcast channels. A partial broadcast channel is a point-to-multipoint channel that enables a sender to send the same message simultaneously and privately to a fixed subset of receivers. We study secret sharing schemes with partial broadcast channels, called partial broadcast secret sharing schemes. We show that a necessary and sufficient condition for the partial broadcast channel allocation of a (t, n)-threshold partial secret sharing scheme is equivalent to a combinatorial object called a cover-free family. We use this property to construct a (t, n)-threshold partial broadcast secret sharing scheme with O(log n) partial broadcast channels. This is a significant reduction compared to n point-to-point channels required in a conventional secret sharing scheme. Next, we consider communication rate of a partial broadcast secret sharing scheme defined as the ratio of the secret size to the total size of messages sent by the dealer. We show that the communication rate of a partial broadcast secret sharing scheme can approach 1/O(log n) which is a significant increase over the corresponding value, 1/n, in the conventional secret sharing schemes. We derive a lower bound on the communication rate and show that for a (t,n)-threshold partial broadcast secret sharing scheme the rate is at least 1/t and then we propose constructions with high communication rates. We also present the case of partial broadcast secret sharing schemes for general access structures, discuss possible extensions of this work and propose a number of open problems.

Goal-programming-assisted visual cryptography method with unexpanded shadow images for general access structures

This paper describes a visual cryptography method for the elimination of pixel expansion and the improvement of contrast. The pro- posed method uses the probability concept to construct a multiobjective linear programming model for general access structures. Then, the so- lution space of the model is explored by goal programming. The advan- tages of the proposed method are fourfold. First, it can avoid expanding the shadow images. Second, it can reach better contrast. Third, it can deal with general access structures and get the desired contrast levels. Fourth, it can be easily extended to deal with the problems of multiple secret images. Experiments on several access structures show that the proposed method is effective against pixel expansion and is capable of contrast improvement. © 2006 Society of Photo-Optical Instrumentation

All Inequalities for the Relative Entropy

The relative entropy of two n-party quantum states is an important quantity exhibiting, for example, the extent to which the two states are different. The relative entropy of the states formed by reducing two n-party to a smaller number $m$ of parties is always less than or equal to the relative entropy of the two original n-party states. This is the monotonicity of relative entropy. Using techniques from convex geometry, we prove that monotonicity under restrictions is the only general inequality satisfied by relative entropies. In doing so we make a connection to secret sharing schemes with general access structures. A suprising outcome is that the structure of allowed relative entropy values of subsets of multiparty states is much simpler than the structure of allowed entropy values. And the structure of allowed relative entropy values (unlike that of entropies) is the same for classical probability distributions and quantum states.

Distributed Ring Signatures from General Dual Access Structures

In a distributed ring signature scheme, a subset of users cooperate to compute a distributed anonymous signature on a message, on behalf of a family of possible signing subsets. The receiver can verify that the signature comes from a subset of the ring, but he cannot know which subset has actually signed. In this work we use the concept of dual access structures to construct a distributed ring signature scheme which works with vector space families of possible signing subsets. The length of each signature is linear on the number of involved users, which is desirable for some families with many possible signing subsets. The scheme achieves the desired properties of correctness, anonymity and unforgeability. We analyze in detail the case in which our scheme runs in an identity-based scenario, where public keys of the users can be derived from their identities. This fact avoids the necessity of digital certificates, and therefore allows more efficient implementations of such systems. But our scheme can be extended to work in more general scenarios, where users can have different types of keys.

A new visual cryptography scheme for STS based access structures

Visual Cryptography Scheme (VCS) for general access structure was developed by Ateniese, Blundo, Santis and Stinson in 1996 for black and white image and subsequently different schemes have been developed. In this paper, we propose a new model for Steiner Triple Systems (STS) based access structures by using “stacking” i.e. “superimposition” and “machine operation” which are mathematically equivalent to “OR” and “XOR” respectively. The concept of qualified set is extended. The technique to construct the VCS is developed for the model. The structure of the VCS is analysed. The contrast of the reconstructed secret image (SI) under the two operations is studied. Finally we introduce STS based (3, n)-Visual Threshold Scheme (VTS) and derive the ratio of its pixel expansion and the number of qualified sets.

Multi secret image color visual cryptography schemes for general access structures *

Abstract In the proposed visual cryptography schemes for general access structures, the single secret image black-and-white visual cryptography schemes with meaningful shares have been constructed, in which the shares are innocent looking images. The meaningful shares have not been realized in single secret image color schemes; neither have the multi secret images color schemes. In this paper, the multi secret images color visual cryptography schemes for general access structures with meaningful shares are constructed by the method of matrix concatenation, the pixel expansion is obtained, and the validity of the scheme is proven. In our scheme, the different combination of meaningful color shares can be used to recover distinct color secret images. The multi secret images black-and-white visual cryptography scheme is a special case of our color scheme. *Supported by National Natural Science Foundation of China (Grant No. 90304014) and the Major State Basic Research Development Program of China (Grant No. ...

Multi-Secret Sharing Scheme Based on the General Access Structure

Multi-Secret Sharing Scheme Based on the General Access Structure

Strongly secure ramp secret sharing schemes for general access structures

Ramp secret sharing (SS) schemes can be classified into strong ramp SS schemes and weak ramp SS schemes. The strong ramp SS schemes do not leak out any part of a secret explicitly even in the case that some information about the secret leaks out from some set of shares, and hence, they are more desirable than the weak ramp SS schemes. In this paper, it is shown that for any feasible general access structure, a strong ramp SS scheme can be constructed from a partially decryptable ramp SS scheme, which can be considered as a kind of SS scheme with plural secrets. As a byproduct, it is pointed out that threshold ramp SS schemes based on Shamir's polynomial interpolation method are not always strong.

Practical secret sharing scheme realizing generalized adversary structure

Most existing secret sharing schemes are constructed to realize general access structure, which is defined in terms of authorized groups of participants, and is unable to be applied directly to the...

Bounds and constructions for unconditionally secure distributed key distribution schemes for general access structures*1

In this paper we investigate the issues concerning the use of a single server across a network, the key distribution center (KDC) to enable private communications within groups of users. After providing several motivations, showing the advantages related to the distribution of the task accomplished by this server, we describe a model for such a distribution, and present bounds on the amount of resources required in a real-world implementation: random bits, memory storage, and messages to be exchanged. Moreover, we introduce a linear algebraic approach to design optimal schemes distributing a KDC, and we point out that some previous constructions belong to the proposed framework.

Bounds and constructions for unconditionally secure distributed key distribution schemes for general access structures

In this paper we investigate the issues concerning the use of a single server across a network, the key distribution center (KDC) to enable private communications within groups of users. After providing several motivations, showing the advantages related to the distribution of the task accomplished by this server, we describe a model for such a distribution, and present bounds on the amount of resources required in a real-world implementation: random bits, memory storage, and messages to be exchanged. Moreover, we introduce a linear algebraic approach to design optimal schemes distributing a KDC, and we point out that some previous constructions belong to the proposed framework.

Weighted decomposition construction for perfect secret sharing schemes

The purpose of this paper is to present a new decomposition technique, called the weighted decomposition construction, for perfect secret sharing schemes with general access structures. This construction is more general than previous constructions. Based on the weighted decomposition construction, we improve the information rates in four cases out of the 18 cases of secret sharing schemes left unsolved for connected graphs on six vertices.

Secret Sharing Schemes with Detection of Cheaters for a General Access Structure

In a secret sharing scheme, some participants can lie about the value of their shares when reconstructing the secret in order to obtain some illicit benefit. We present in this paper two methods to modify any linear secret sharing scheme in order to obtain schemes that are unconditionally secure against that kind of attack. The schemes obtained by the first method are robust, that is, cheaters are detected with high probability even if they know the value of the secret. The second method provides secure schemes, in which cheaters that do not know the secret are detected with high probability. When applied to ideal linear secret sharing schemes, our methods provide robust and secure schemes whose relation between the probability of cheating and the information rate is almost optimal. Besides, those methods make it possible to construct robust and secure schemes for any access structure.

Theory of quantum secret sharing

I present a variety of results on the theory of quantum secret sharing. I show that any mixed state quantum secret sharing scheme can be derived by discarding a share from a pure state scheme, and that the size of each share in a quantum secret sharing scheme must be at least as large as the size of the secret. I show that the only constraints on the existence of quantum secret sharing schemes with general access structures are monotonicity (if a set is authorized, so are larger sets) and the no-cloning theorem. I also discuss some aspects of sharing classical secrets using quantum states. In this situation, the size of each share can sometimes be half the size of the classical secret.

General information dispersal algorithms

We analyse the problem of distributing pieces of a file f among a set of users in such a way that some predefined subsets of users can, pooling together their pieces, reconstruct the entire file f. We call access structure the set of all qualified subsets and we show how to extend the notion of information dispersal algorithms proposed by Rabin (1989, 1990) to general access structures. We give bounds on the amount of information each participant must have. Then, we apply this results to construct optimal or near to optimal schemes for general access structures. Finally, we consider an application of our results to cryptography.

Visual Cryptography for General Access Structures

A visual cryptography scheme for a set P of n participants is a method of encoding a secret image SI into n shadow images called shares, where each participant in P receives one share. Certain qualified subsets of participants can “visually” recover the secret image, but other, forbidden, sets of participants have no information (in an information-theoretic sense) on SI . A “visual” recovery for a set X ⊆ P consists of xeroxing the shares given to the participants in X onto transparencies, and then stacking them. The participants in a qualified set X will be able to see the secret image without any knowledge of cryptography and without performing any cryptographic computation. In this paper we propose two techniques for constructing visual cryptography schemes for general access structures. We analyze the structure of visual cryptography schemes and we prove bounds on the size of the shares distributed to the participants in the scheme. We provide a novel technique for realizing k out of n threshold visual cryptography schemes. Our construction for k out of n visual cryptography schemes is better with respect to pixel expansion than the one proposed by M. Naor and A. Shamir (Visual cryptography, in “Advances in Cryptology—Eurocrypt '94” CA. De Santis, Ed.), Lecture Notes in Computer Science, Vol. 950, pp. 1–12, Springer-Verlag, Berlin, 1995) and for the case of 2 out of n is the best possible. Finally, we consider graph-based access structures, i.e., access structures in which any qualified set of participants contains at least an edge of a given graph whose vertices represent the participants of the scheme.

An explication of secret sharing schemes

This paper is an explication of secret sharing schemes, emphasizing combinatorial construction methods. The main problem we consider is the construction of perfect secret sharing schemes, for specified access structures, with the maximum possible information rate. In this paper, we present numerous direct constructions for secret sharing schemes, such as the Shamir threshold scheme, the Boolean circuit construction of Benaloh and Leichter (for general access structures), the vector space construction of Brickell, and the Simmons geometric construction. We discuss the connections between ideal schemes (i.e., those with information rate equal to one) and matroids. We also mention the entropy bounds of Capocelli et al. Then we give a very general construciton, called the decomposition construction, and numerous applications of it. In particular, we study schemes for access structures based on graphs and the many interesting bounds that can be proved; and we determine the exact value of the optimal information rate for all access structures on at most four participants.

Secret sharing scheme realizing general access structure

AbstractAs a method of sharing a secret, e.g., a secret key, Shamir's (k, n) threshold method is well known. However, Shamir's method has a problem in that general access structures cannot be realized. This paper shows that by providing the trustees with several information data concerning the distributed information of the (k, n) threshold method, any access structure can be realized. the update with the change of the secret trustees and the relation to the threshold graph are also discussed.